A Faraday Cage should give some protection from an EMP - you could probably build a good one for very little money.
There would certainly be differences between HDD and SSD, which I'll be interested to hear about.
Depending on the size of the digital information that you want to store then I'd be inclined for going for a solution that would also give you redundancy (i.e. multiple copies of your data spread over multiple faraday cages)
